and \(\kappa ^2 = 8\pi G_{N}\) , and \(G_{N}={ M_P}^{-2}\)  is the (3+1)-dimensional Newton constant (with \(M_{P}= 1.22 \times 10^{19}\)  GeV the four-dimensional Planck mass). The \(\dots \)  denote in particular higher derivative terms in the dilaton field and \(\Omega \)  is related to the cosmological constant. The constant \(G_{N}\)  is related to the string mass scale \(M_s\)  via [1]}: \({G_{N}}^{-1} = {\mathcal {V}}^{(n)} \, M_s^{2+n}\) , with \({\mathcal {V}}^{(n)}\)  a compactification volume (or appropriate bulk volume factor, in brane-universe scenarios).
In the closed string sector, \(B_{\mu \nu }\)  is a gauge field with a gauge symmetry
\(B_{\mu \nu } \rightarrow B_{\mu \nu } + \partial _\mu \theta _\nu - \partial _\nu \theta _\mu \)  which characterises the target-space effective action. This implies that
the action depends only on the field strength of the field \(B_{\mu \nu }\) , which is a three-form with components
\(H_{\mu \nu \rho } = \partial _{[\mu }\, B_{\nu \rho ]},\) 
